Advertisements
Advertisements
Question
Factorise:
8p3 −\[\frac{27}{p^3}\]
Advertisements
Solution
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ 8p^3 - \frac{27}{p^3}\]
\[ = \left(2p \right)^3 - \left(\frac{3}{p}\right)^3\]
\[ = \left(2p - \frac{3}{p} \right)\left\{\left(2p \right)^2 + \left( \frac{3}{p} \right)^2 + \left(2p \right) \times \left(\frac{3}{p} \right) \right\}\]
\[ = \left(2p - \frac{3}{p} \right)\left(4 p^2 + \frac{9}{p^2} + 6 \right)\]
RELATED QUESTIONS
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Factorise:
27m3 − 216n3
Factorise:
125y3 − 1
Simplify:
(x + y)3 − (x − y)3
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify:
(a + b)3 − a3 − b3
Factorise the following:
27x3 – 8y3
